Justice Clarence Thomas, acting alone, granted the temporary stay pending a further decision by himself or the full court.
Missouri state law forbids spending tax dollars to facilitate an abortion. However, U.S. District Judge Dean Whipple ruled Thursday that the prison system was blocking the woman from exercising her right to an abortion and ordered that the woman be taken to the clinic Saturday.
An appeals court on Friday refused to stay the ruling.
The woman, whose name was not disclosed in court papers, has said she will borrow money for the abortion from friends and family, but cannot afford to pay for transportation.
Under a policy adopted in July, Missouri's prison system does not provide transportation or security for inmates seeking abortions. The policy is based on a state law that prohibits the spending of public funds "for the purpose of performing or assisting an abortion not necessary to save the life of the mother."